where \(\nu >0\) , \(0\le \alpha <d\)  and \(\mathcal {S}\)  is a sparse collection [1]} of dyadic cubes in the sense that
\(\exists \,\Lambda _0 \in (0,1)\ s.t.\ \, \large |\bigcup _{P\in {\mathbb {P}(Q)\cap \mathcal {S}}}P\large |\le \frac{1}{\Lambda _0}|Q|. \) 

